1/3x+4/5x=34

Solution for 1/3x+4/5x=34 equation:

1/3x+4/5x=34

We move all terms to the left:

1/3x+4/5x-(34)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


5x/15x^2+12x/15x^2-34=0

We multiply all the terms by the denominator


5x+12x-34*15x^2=0

We add all the numbers together, and all the variables

17x-34*15x^2=0

Wy multiply elements

-510x^2+17x=0

a = -510; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-510)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-510}=\frac{-34}{-1020}
=1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-510}=\frac{0}{-1020}
=0
$